/*
提交链接：https://leetcode.cn/problems/delete-operation-for-two-strings/submissions/562542716
583. 两个字符串的删除操作-中等
完成日期：2024/9/8
线性dp
*/

class Solution {
public:
    int minDistance(string word1, string word2) {
        int m = word1.size();
        int n = word2.size();
        // 创建一个二维 dp 数组
        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
        // 填充 dp 数组
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (word1[i - 1] == word2[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                } else {
                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
                }
            }
        }
        // 最长公共子序列的长度
        int lcsLength = dp[m][n];
        // 计算最小步数
        return m + n - 2 * lcsLength;
    }
};